Transformations, trajectories, and similarities of national production structures: A comparative fingerprinting approach

This article proposes a network-analytical framework for the comparative study of national production structures in global production networks. Conceptualizing such structures as the linked networks of both domestic and foreign intermediate inputs, the latter constituting the characteristic feature of contemporary economic globalization, the proposed approach extracts a structural profile that captures the up- and downstream prominence of economic sectors for a particular country and year. These ‘fingerprints’ of national production structures can subsequently be compared on a pairwise basis, providing novel ways to determine and compare the structural similarities, transformations, and trajectories of national economies in the transnational production regime. Two shorter case studies exemplify the approach. The first applies clustering methods to explore spatiotemporal similarities of the production structures for 40 countries over the 1995–2011 period. Based on such similarities, an analytically useful classification into 11 structural types is proposed. The second study addresses structural transformations and trajectories during EU’s eastern enlargement, finding significant structural change, yet minuscule East-West convergence.

Appendix A: Tables and metadata   A

A.3 Data coverage in WIOD13
Examining the national Input-Output tables in WIOD (2013 release) for all countries and years, the following 7 country-sectors have zero reported inputs for all years in the 1995-2011 period.This corresponds to 0.5% of all sectorial time-series in WIOD13, with 30 out of 34 sectors (88%) having complete data for all countries and years.Although these definitely constitute missing data, these were nevertheless treated as zero values when determining the pair-wise dissimilarity between two fingerprints.Of the 680 potential fingerprints in WIOD13, i.e. covering 40 countries for 17 years, 27 of these were however excluded from all analyses due to their eigenvalue diagnostics.See Appendix D.1.

B.3 Average cluster distances
Total number of national fingerprints for each cluster given by NFP; number of countries represented in each cluster given by NC.See Appendix B1 for cluster membership tables.By dividing the dominant eigenvalues with the second-largest eigenvalues for each of the up-and downstream eigenvectors, we obtain the second eigenvalue diagnostics for up-and downstream eigenvectors: u1vs2 and d1vs2.Mean, median and value ranges for these diagnostics are given in Table 4, with their distributions given in Figure 2.  The mean and median eigenvalue diagnostics are relatively good, but there are indeed several fingerprints where either one or both of its eigenvectors have corresponding eigenvalue diagnostics that are low.For those where both of the dominant eigenvectors have low diagnostics, Portugal's 1995 fingerprint has the objectively worst diagnostics (u% = 15.5%;u1vs2 = 1.13; d% = 18.5; d1vs2 = 1.20), with Turkey 2000 as a good contender for the second worst (u% = 17.9%; u1vs2 = 1.21; d% = 18.3; d1vs2 = 1.17).
Portugal 1995 and Turkey 2000 stick out with both their diagnostic measures being very low, which is not the case for the vast majority of fingerprints.If we set an acceptable threshold for the 1 st share diagnostic measures (i.e.u% and d%) to 20 percent and a corresponding threshold for the 1 st vs. 2 nd ratio diagnostic measure(i.e.u1vs2 and d1vs2) to 1.25, the number of fingerprints with combinations of acceptable diagnostic measures for their up-and downstream components are as given in Table 5 below.With Portugal 1995 and Turkey 2000 being part of both the 21 fingerprints with sub-par upstream diagnostics and the 8 with sub-par downstream diagnostics, there are a total of 27 fingerprints with potentially problematic eigenvector components -see Table 6 below.These fingerprints should thus be interpreted with particular care, and they are therefore removed from the analyses presented in the paper.Czech Rep. 2005, 2009Portugal 1995-1996, 2009-2011Germany 2006-2008, 2011Slovakia 2004-2005, 2009-2011 Ireland 2008 Turkey 2000 These thresholds could be criticized as being too liberal, with the implication that one should be even more careful in interpreting the dominant eigenvectors and the obtained fingerprints of upand downstream sectorial prominence for a larger set of fingerprints.Still, even with sporadically low eigenvalue diagnostic measures for particular fingerprints, these do not seem to interfere much with results from comparative fingerprinting analysis.The case in point is the cluster analysis done in this study (see Section 3.1 in manuscript, particularly Figure 11): although specific fingerprints indeed have rather poor eigenvalue diagnostics, these fingerprints nevertheless seem to capture enough structural features of their economies to result in longitudinally consistent clusters that make sense.

D.2 Analyzing structural trajectories using multidimensional scaling: the case of the European Union 1995-2011
Given a set of fingerprints and their pairwise dissimilarity/distance metrics, the first case study in the article demonstrates how such a matrix could be analyzed using hierarchical clustering.Whereas this approach provides a way to separate entities into discrete, nominal subsets, such distance data could also be approached using the family of techniques for dimensionality reduction, which maps dissimilarity/distance data into (typically) two or three dimensions.Classical multidimensional scaling (MDS; also known as principal coordinates analysis) constitutes one such alternative tool for mapping out similarity patterns and potential latent variables, as well as tracking the developmental trajectories of such structures over time, in a more continuous, non-categorical way.
Building on the second case study in the article, concerning the Eastern enlargement of the European Union, all ten Central-and East-European countries were initially included (i.e.Bulgaria, Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia, and Slovenia), together with five of the six founding members of the European Union (i.e.Belgium, France, Germany, Italy, and the Netherlands).Covering 15 countries over 17 years, though here also excluding 12 country-year fingerprints due to low Eigenvalue diagnostics, Euclidean distances for each pair of these 243 country-year fingerprints were calculated.Classical metric multidimensional scaling (MDS) was applied to this dissimilarity matrix to extract both 2-and 3-dimensional solutions.Evaluating these solutions with the Kruskal stress index, the 2-dimensional solution resulted in a high stress of 0.49, dropping to 0.30 for the 3-dimensional solution.Further exploration revealed that it was particularly Estonia's inclusion that contributed to this stress.Redoing the MDS with Estonia excluded, i.e. with a total of 14 countries and 226 country-year fingerprints, the Kruskal stress went down to 0.43 for the 2-dimensional solution and 0.27 for the 3-dimensional solution.As the 3dimensional solution lies below the generally acceptable threshold (0.3), this solution was chosen for further exploration.
Calculating 3-year simple-moving-average coordinates for all years (using 2-year averages for 1995 and 2011, respectively), Figure 3 depicts the first two dimensions of the 3-dimensional MDS solution.
Whereas this figure can be perceived as looking at the 3-dimensional solution from the side (like the side of a cube), the supplementary figure (Figure 4) looks at the same data but from "above" (like you are leaning forward into the paper surface and looking down).Whereas the 3 rd dimension indeed is necessary to bring down the Kruskal stress index to reasonable levels (i.e.0.27), the first two dimensions (Figure 3) does seem to allow for some interesting interpretations.First, corroborating findings from the two case studies in the article, the production structures of these five Western economies are relatively similar and stable over time.Although both Hungary and Czech Republic exhibit movement towards the 'Western' cluster, a notable aspect of Figure 3 is the lack of East-West structural convergence.As concluded from the longitudinal plots in the paper (see Figures 16 and 17 in the manuscript), the transformations of the 'Eastern' production structures did not markedly affect the average structural dissimilarity between the two regions.This finding is well reflected by the first two dimensions of the MDS solution above: despite a significant transformation of several of the Eastern production structures during this period, they seem to remain equidistant to their 'Western' counterparts.Additionally, albeit relatively short, the trajectories of the 'Western' structures seem to move them further away from their Eastern neighbors.
Multidimensional scaling could potentially be a useful supplement to the existing tools for fingerprint analysis proposed in this article.However, similar to all such techniques, it is of course imperative that relevant goodness-of-fit measures, such as the Kruskal stress index here, remain within acceptable boundaries.In the context of fingerprinting, tentative explorations of the WIOD13-based fingerprints seem to indicate that three dimensions are needed to arrive at such acceptable levels.Thus, the visualization and interpretation of such rescaled data should then preferably instead be done through interactive and/or virtually augmented/VR tools.

Figure 1 :
Figure 1: Distribution of dominant eigenvalues for up-and downstream eigenvectors

Figure 2 :
Figure 2: Distribution of 1 st vs. 2 nd eigenvalue ratios for up-and downstream eigenvectors Their structural trajectories are overall unidirectional, more linear, and seemingly ending up closer to each other in 2011 compared to 1995.In contrast, most of the 'Eastern' production structures experience dramatic structural transformations.The structural trajectories of Bulgaria, Latvia, Hungary and Poland are particularly notable, traversing large distances in this 'structural space'.Lithuania, and perhaps also Hungary, seem to experience retrograde structural trajectories, but Lithuania, together with Romania, do not move very far away from their starting position.This is in line with the sequence index plot of the 11-type classification (see Figure11in manuscript): of the seven 'Eastern' countries starting off as 'Agriculture & Food'-type economies in 1995, only Lithuania and Romania remain as this type throughout the 1995-2011 period.

Table 1 :
Average within-and between-cluster distance for the 5-cluster partition derived from the (unweighted) average-

Table 2 :
Average within-and between-cluster distance for the 11-cluster partition derived from the (unweighted) average-Percentages in brackets indicate the 1 st share eigenvalue diagnostics: on average, u% and d% are 27 and 29 percent respectively, with their medians being slightly lower.

Table 3 :
Statistics on sizes and shares of dominant eigenvalues for up-and downstream eigenvectors

Table 4 :
Statistics on ratio between dominant and second-largest eigenvalues for up-and downstream eigenvectors

Table 5 :
Frequency table for acceptable eigenvalue diagnostic measures

Table 6 :
Country-year fingerprints excluded from the analyses